The present invention relates to meteorological techniques for estimating a precipitation rate by means of a radar.
For cost reasons, the radars of the European network operate in C-band, a frequency which is substantially attenuated on traversing internal rains, this making the retrieval of the precipitation rate much trickier than in S-band where the attenuation effects are more limited.
In applications to urban hydrology, the X-band is even envisaged, but attenuation by rain then plays a very important role, and it becomes crucial to take it into account.
In this regard, reference may advantageously be made to their publication: HITSCHFELD-BORDAN, 1954, xe2x80x9cErrors inherent in the radar measurement of rainfall at attenuating wavelengthsxe2x80x9d, J. Meteor, 11, pp. 58-67. Unfortunately, in an actual application where the data are noisy and where one may be in the presence of a calibration error (even a small one), this solution turns out to be numerically unstable.
To alleviate this drawback, a proposal has already been made to operate under polarization diversity and to utilize the differential reflectivity ZDR, which is the ratio of the reflectivities under H and V polarization.
As it falls, a raindrop undergoes aerodynamic flattening, the consequence of which is that its scattering cross section is larger for H polarization than for V polarization. In a radar operating at attenuated frequency, the parameter ZDR results from two effects with opposite tendencies: on the one hand, the effect of differential backscattering (which tends to increase ZDR with the mean size of the drops), and on the other hand, the effect of differential attenuation (with the opposite tendency).
For a recent example of determining a precipitation rate from a dual-polarization radar, reference may advantageously be made to patent application FR-2 742 876, as well as to the publication: xe2x80x9cPolarimetric Radar at Attenuated Wavelenghts as a Hydrological sensorxe2x80x9dxe2x80x94M. SAUVAGEOTxe2x80x94Journal of etmosyheric and oceanic technologyxe2x80x94vol. 13xe2x80x94p. 630-637, 1996.
However, it is not easy to measure the coefficient ZDR.
The dynamic range of variation of ZDR is around 1 to 2 and therefore covers a few dB at the very most. Furthermore, this measurement requires cross-calibration of the H and V channels to within a tenth of a dB; integration over numerous independent samples so as to temper the statistical fluctuation of the signal, and a very good performance of the antenna (sidelobes at 30 dBxe2x80x94outwardxe2x80x94below the main lobe).
Alternatively, there has also been a proposal, in particular in the publication: xe2x80x9cDifferential propagation phase shift and rainfall rate estimationxe2x80x9dxe2x80x94M. SACHINANDA, D.S. ZRNICxe2x80x94Radio sciencexe2x80x94vol. 21, no. 2, p. 235-247, March-April 1986. to utilize another parameter, namely the differential phase (denoted "PHgr"dp). This is because the flattening of the raindrop does not affect only the backscattering cross section inducing the asymmetry "sgr"H greater than "sgr"V (where "sgr"H and "sgr"V represent the cross sections for H and V polar, respectively), but also the propagation of the radar wave whose wave vector is affected as much in respect of its imaginary part (the specific attenuation is greater for H polarization than for V polarization, differential attenuation effect mentioned earlier), as in respect of its real part (where the asymmetry between H and V translates into a differential variation of the phase along the path. In actual fact, the derivative of "PHgr"dp along the radius (rate of variation of "PHgr"dp denoted Kdp) is almost proportional to the precipitation rate (and hence "PHgr"dp, to the integrated precipitation rate), which explains the benefit of measuring it.
The estimator of Kdp exhibits numerous advantages: it is insensitive to attenuation along the path; it is insensitive to a radar calibration error; it is much less affected than ZDR by the sidelobes of the antenna; it is entirely unaffected by partial masking of the antenna beam (which occurs routinely when operating at low elevation).
However, it exhibits the major drawback of being greatly affected by noise since it results from differentiating "PHgr"dp along the beam. The measurement of Kdp therefore requires a long integration time, which is incompatible with the hydrological application which demands fast scanning of the radar beam.
For its part, the invention proposes a technique which makes it possible to alleviate the drawbacks of the prior techniques and which implements simple processing which is reliable and robust, in particular with regard to the statistical measurement noise (thereby allowing fast scanning).
More particularly, the invention proposes a process for estimating a precipitation rate by means of a bipolar radar, characterized by the following various steps:
the differential phase "PHgr"dp and the attenuated reflectivity Z according to at least one of the polarizations H or V are measured by means of said bipolar radar, over a given interval [r1, r0] of path radius r with respect to said radar,
an estimate of the value K(r0) of the attenuation at r0 is determined from the attenuated reflectivity profile thus measured, as well as from the difference in the differential phase between r0 and r1;
an estimate K(r) of the specific attenuation at r as a function of the attenuation K(r0) thus determined and of the attenuated reflectivity profile Z(r) is determined;
the rate of precipitation R(r) is determined knowing K(r).
Advantageously, an estimate of the value K(r0) of the attenuation r0 is determined from the equation             K      ⁢              (                  r          0                )              ⁢                  ∫                  r          1                          r          0                    ⁢                                                  Z              b                        ⁢                          (              s              )                                                                          Z                b                            ⁢                              (                                  r                  0                                )                                      +                                          K                ⁢                                  (                                      r                    0                                    )                                            ·                              I                ⁢                                  (                                      s                    ,                                          r                      0                                                        )                                                                    ⁢                  ⅆ          s                      =      γ    ·          (                                    φ            dp                    ⁢                      (                          r              0                        )                          -                              φ            dp                    ⁢                      (                          r              1                        )                              )      
where:
      I    ⁡          (              s        ,                  r          0                    )        =      0.46    ⁢    b    ⁢                  ∫                  r          1                          r          0                    ⁢                                    Z            b                    ⁡                      (            u            )                          ⁢                  xe2x80x83                ⁢                  ⅆ          u                    
and b is the exponent of the power relation
K(r)=aZ(r)b
xe2x80x83and where xcex3 is the parameter of proportionality between the specific attenuation and the differential rate of variation of the phase.
Preferably, an estimate K(r) of the specific attenuation is determined as a function of r from the equation                               Z          b                ⁢                  (          r          )                            K        ⁢                  (          r          )                      -                            Z          b                ⁢                  (                      r            0                    )                            K        ⁢                  (                      r            0                    )                      =            I      ⁢              (                  r          ,                      r            0                          )              .  
Advantageously, the attenuated reflectivity Z is measured for both of the two polarizations H or V and the precipitation rate R(r) for a given path radius r is determined for both of these two polarizations.
The invention also relates to a device for estimating a precipitation rate comprising a bipolar radar, as well as processing means, characterized in that said radar comprises means for measuring the differential phase "PHgr"dp and the attenuated reflectivity Z according to at least one of the polarizations H or V and in that the processing means implement the various processing steps of the process according to claim 1.